• 



T/US3 
.6/5 



! .US'' 



.y,*b, Bureau of Yards and Docks, 

Navy Department, 
Washington, D. C, January 1, 1918. 

STANDARDS OF DESIGN, REINFORCED CONCRETE. 



Details of construction. 

1. Materials, methods of mixing, placing and finishing, character of 
forms, inspc tion, etc., shall be in strict accordance with the require- 
ments of Navy Standard Specification, concrete and mortar 59C2q 

2. lrotective covering.— The minimum thickness of concrete or 
mortar for protection of metal against corrosion shall be 1 inch 

The minimum thickness of concrete or mortar for protection of 
metal against fire shall be as follows: 

., Inches. 

Columns and girders 2 

Floor beams i i /o 

Slabs ".".WW" '.':"'."'.'.'.'.'.[ ."!.\\\\\\ i 

The above dimensions are from face of rod to face of concrete To 
determine distance from face of concrete to center of steel add half 
the diameter of the rods to the above dimensions. 

. All corners and edges of columns, girders, and beams shall be either 
beveled or rounded. 

3. Splicing reinforcing material and joints in reinforced concrete con- 
struction—Where tension or compression reinforcement is spliced it 
shall be lapped on the basis of the bond stress and the stress in the 
bar at the point of splice, or a connection shall be made between the 
bars of sufficient strength to carry the stress. 

In columns, small rods (3/4 inch and under) shall be lapped as 
specified above, and structural shapes or heavy bars shall be properly 
spliced and provided with bearing plates at foundations; rods 
above 8/4 inch shall be squared and butted in sleeves, and in foun- 
dations, or the bars shall be carried into the footing a sufficient 
distance to transmit the stress of the steel to the concrete by means 
of the bond resistance. 

4. Stopping points .—Whenever it is found impossible, owing to 
the magnitude of the work, to cast the entire structure in one opera- 
tion, the following locations shall govern for stopping points for the 
respective parts: Joints in columns shall be hush with bottom 

{surface of girders, and in fiat slab construction at the bottom of the 
fiare of the column head; joints in girders shall be at center of span 
unless a floor beam intersects the girder at this point, in which case 
the joint shall be offset a distance equal to at least twice the width 
of the beam ; joints in floor beams and slabs shall be at the center of 
; the span All joints shall be perpendicular to the axis or surface of 
♦the member jointed In every case planes of cleavage caused by 
stoppage of work shall be provided with offsets and extra reinforce- 
ment, it necessary, to develop the full designed strength 



41321—18 



?-z 






3 



5. General assumptions. -Slabs and floor beams shall ^ designed 
to support the total dead and live loads; girders shall be designed to 
support the total dead load and 80 per cent of the live ^ loac L and 
columns shall be designed for the total dead load and Jf per ceiit of 
the live load, except as noted below. For roof loads the full lie 
load shall be used In storehouses 80 per cent of the live load 
hall be used on columns only: beams and girders shall carry full 
ive load Proper provision shall be made for the dynamic effect 
of live load, wh P ere Le justifies consideration, by the addition o^a 
percentage. In special cases, where conditions justify , girdeis.na 
?olunms shall be designed for 100 per cent of the live load in addi- 

^S^^tAearns, and f ders and f^W^ 

a maximum span length of the clear distance between supports plus 
KXo&er or slab. For continuous or restrained beams 
the span length shall be taken as the clear distance between faces of 
suppoS exclusive of brackets. The length of column shall be taken 
as the maximum unsupported length. 
7. Spaaing ofrods.-The lateral spacing of paralM barsjhall not 

ss than 3 diam 

eters from sicl« 

een 2 layers of 
more than 2 layers win not oe auwcu uu^- - -— , 

same imperative, in which case special provisions shall be made 



77 Spacing cf rods. -The lateral spacing ot parallel «u^ 
be less than 3 diameters from center to center and not less than 2 
diameters from side of beam to center of rod The clear space 
between 2 lavers of bars shall not be less than 1 inch. Ihe use ot 
morTthan 2 layers will not be allowed unless *1^™*™» ^ 
. .J.- __ :„ ^-u;„\, ™ aa . cnona nrovisions siiall De maue 



for 8 t3 cSf«S^For columns reinforced longitudinally and with or 
without qX hooping, the ratio of "-^ d ^* of ™hnnn 
to its least over-aU diameter shall not exceed lo. lor commua 
einforcld 8 w?i spiral hooping only, **^^^*fi?^ 
In no case shall the least over-all diameter be less t nan 1. ^cnes^ 
ThP protective covering over the steel shall be 4 incnes. ine 
efilctTe area "l hooped-columnB.8h.il be >**%£*$£&£*& 

area The total amount of spiral or hooping romtorcemen shall not 
of the Inclosed column, and shall in no case be greater than 2 1/2 

D. of 
22 IS 



^^ 3 

eight times the thickness of the slab; also it shall not exceed, four 
times the width of the stem. For isolated beams the width of the 
flange shall not exceed three times the width of the stem. In all 
cases the total width of flange shall not exceed one-fourth of the 
length of the span. 

11. Maximum allowable unit stresses and ratio of moduli of elas- 
ticity. — The allowable unit stresses shall be the percentages given 
herein of the ultimate strength of the particular concrete which is 
to be used, "as shown in the following: 



Table of ultimate compressive strengths of different mixtures of concrete. 
[In pounds per square inch.] 



Aggregate. 


1:1:2 


1:H:3 1:2:4 


1:2§:5 


1:3:6 


Granite, trap rock gravel, hard limestone, and 


3,000 

2,200 

800 


2,500 

1,800 

700 


• 

2,000 

1,500 

600 


1,600 

1,200 

500 


1,300 
1,000 




Cinders 


400 











ALLOWABLE UNIT STRESSES FOR PIERS AND FOUNDATIONS. 

(a) Plain bearing on a concrete surface of at least twice the loaded 
area, 85 per cent of compressive strength. 

(6) Plain bearing on other surfaces, 25 per cent of compressive 
strength. 

(c) Axial compression in a plain concrete pier, the length of which 
does not exceed four diameters, 22.5 per cent of compressive 
strength. 

ALLOWABLE UNIT STRESSES FOR SLABS, BEAMS, AND GIRDERS. 

(d) Compression in extreme fibers of concrete, 32.5 per cent of 
compressive strength. 

(e) Compression in extreme fibers of concrete at supports of con- 
tinuous beams, 37.5 per cent of compressive strength. 

(/) Vertical shearing stress, horizontal bars only and without web 
reinforcement, 2 per cent of compressive strength. 

(<7) Vertical shearing stress, bent-up bars only and without vertical 
stirrups, 8 per cent of compressive strength. 

(h) Vertical shearing stress, combination of bent-up bars and 
vertical stirrups fastened securely to the bars and spaced horizon- 
tally not more than one-half of the depth of the beam, 5 per cent of 
compressive strength. 

(*) Punching shear with diagonal tension provided for, 6 per cent 
of compressive strength. 

The unit shearing stress shall be computed by formula 22, given 
in the appendix. 

In providing for diagonal tension the web reinforcement shall be 
designed to take two-thirds of the total vertical shear. 



/7-£tf53 



ALLOWABLE UNIT BOND STRESS. 

(J) Bond between concrete and plain bars, 4 per cent of compres- 

: Bond h between concrete and deformed bars. 5 per cent of 

C0 " P B^d^e\ r w n e!n concrete and drawn wire, 2 per cent of com- 
pressive strength. 

ALLOWABLE UNIT STRESSES IX COLUMNS. 

(m) Columns with longitudinal bars held by bands, the bars 
bein- not less than 1 per cent nor more than 4 per cent ot the area 
oftne column core, the bands being not less than 1 4 inch m diameter 
and approximatelv 12 inches on centers, shall have a unit stress on 
thl ? concrete core* not to exceed 25 per cent ot the compressive 

£tr T g l h olumns with close hoops or spirals only, of not less than 
1 per cent of the column core and spaced not more than one-sixth 
of the diameter of the column core nor more than 2 12 inches on 
centers, shall have a unit stress on the concrete core not to exceed 
27 per cent of the compressive strength - + v i^^JSLi 

(o) Columns with close hoops or spirals and with longitudinal 
bars all within the limits specified above, shall have a unit stress 
on he concrete core not to exceed 33 1 3 per cent ot the compres- 
sive strength, and in no case to exceed 800 pounds per square inch. 

ALLOWABLE EXIT STRESS IX STEEL REIXFORCEMEXT. 

(v) The tensile or compressive stress in steel shall not exceed 
16 000 pounds per square inch. Steel in compression shall be 
considered to be stressed "n" times the stress in the adjacent con- 
crete, where "n" represents the ratio, of the modulus ot elasticity 
of steel to that of concrete, as given below. 

MODULI OF ELASTICITY. 

In designing reinforced concrete, the ratio of the modulus of 
elasticity of steel to the modulus of elasticity of concrete shall be 

tak 7 D Fonv. when the compressive strength of the concrete does 
not exceed S00 pounds per square inch. 

Fifteen, when the compressive strength ot the concrete is 
greater than 800 pounds per square inch and less than 2,200 pounds 

P Ts .'TweWe^ when the compressive strength of the concrete is 
greater than 2,200 pounds per square inch and less than 2MV 
pounds per square inch. . 

Ten. when the compressive strength ot the concrete is greater 
than 2,000 pounds per square inch. 



12. STANDARD NOTATION. 

RECTANGULAR BEAMS. 

The following notation shall be used: 
/ s = tensile unit stress in steel. 
f = compressive unit stress in concrete. 
-Eg=modulus of elasticity of steel. 
E Q = modulus of elasticity of concrete. 

n== w c 

M— moment of resistance, or bending moment in general, in 

inch-pounds. 
A= steel area in square inches. 

6=breadth of beam in inches. 

£?=depth of beam, to center of steel, in inches. 

£=ratio of depth of neutral axis to effective depth d. 

2=depth of resultant compression below top. 

j=ratio of lever arm of resisting couple to depth d. 
jd=d—z=a,rm of resisting couple. 
p= steel ratio (not percentage). 
w=load per lineal foot of slab or beam. 

Z=length of span in feet. 

T-BEAMS. 

6= width of flange. 
6 / =width of stem. 
i=thickness of flange. 

BEAMS REINFORCED FOR COMPRESSION. 

^4=area of compressive steel. 

p / = steel ratio for compressive steel. 

f s — compressive unit stress in steel. 

C= total compressive stress in concrete. 
C / = total compressive stress in steel. 
6^= depth to center of compressive steel. 

2=depth of resultant of C and C' '. 

SHEAR AND BOND. 

V= total shear. 
v— shearing unit stress. 

it=bond stress per unit superficial area of bar. 
o= circumference or perimeter of bar. 
2 =sum of the perimeters of all bars. 

COLUMNS. 

A= total net area. 
J. s =area of longitudinal steel. 
yl c =area of concrete. 

P= total safe load. 



DESIGN. 



13. Beams and slabs, 
(a) Continuous spans. 

Slabs 5^ id 2 at center and over supports. 
Beams ^ ^':Z 2 at center and over supports for interior spans. 
■£o wl 2 at center and over support for end span of a series. 
Beams and slabs | wl? over center support for 2 spans only. 
-^q ui 2 at center of spans for 2 spans only. 
At ends of continuous beams the amount of negative moment 
depends on the form of construction. 

No smaller moments than the above shall be allowed over supports 
even if more reinforcement is put in at the center of the span. 
Steel on compression side may be considered as acting. 
(b) Ends free and simply supported. 
Beams and slabs ^ wl 2 at center. 
14. Slabs supported along four sides and reinforced in two 
directions. . , , • -, 

(a) Square slabs.— One-half the load shall be considered as carried 
by each svstem of reinforcement. 

(6) Rectangular slabs.— li w is the total load per square foot, 
I and l x are the length and breadth of panel, respectively, m feet 

and r=f-, then the load per square foot carried by the transverse 

i 
system of reinforcement shall be taken as — 

F+l? or l+f 4 

and the load per square foot carried by the longitudinal system shall 
be taken as — 

wlj 4 w 

■ l*+l* OT l+r 4 

Assuming these unit loads as determined above for (a) and (6), 
two-thirds of the calculated moments shall be assumed as carried by 
the center half and one-third by the outside quarters of each system 
of reinforcement. 

15. Stirrups should be spaced by the formula: 

_ lCOCOa 
s ~(r-40)6 

for 1:2:4 concrete where — 

-y=unit shearing stress, see formula (22) of the Appendix. 
&=breadth of beam in inches. 
s=d stance between stirrups in inches. 
a = cross-sectional area of 1 stirrup in square inches. 
;\7 tr.—'\ he unit Bhear on cross section should never exceed 120 
pounds per square inch. . 

If mam reinforcing rods are bent up for web reinforcement, the 
points of bending shall be calculated. For this purpose the method 



used for designing cover plates of built-up steel girders is applicable, 
the formula for uniform load on a simply supported beam being: 



L' la' 



where I/=length of horizontal part of bent rods. 

L =span length. 

a' =area of bent rods. 

A = total area of reinforcement. 
For continuous beams, bending up at the 1/4 points will be satis- 
factory, but sufficient steel must be placed top and bottom, on each 
side of the quarter points, to take care of the stresses resulting from 
irregular loads. 

16. In girders and beams use 1:2:4 concrete and the following 
maximum unit stresses: 



.pounds.. 18,000 
...do.... 650 



shall not 



12,500 
000 



Tension in steel 

Compression in concrete 

This gives — 

M= 0.3786 d 

jd= 0.8738 d 
'J/=107.5 bd 2 

A= 0.0077 bd 

17. Outside work, such as piers, wharves, sea walls, etc. 
exceed the following unit stresses used in their design: 

Tension in steel pounds . 

Compression in concrete do . . . 

This gives — 

M= 108.0 bd 2 

A= 0.01 bd 

hd= 0.418 d 

jd= 0.861 d 

APPENDIX. . 

The formulae given in the above standards are based on the fol- 
lowing general formulas, which were compiled by the committee on 
concrete and reinforced concrete, appointed by the American 
Society of Civil Engineers: 

1. RECTANGULAR BEAMS. 




Position of neutral axis, 



k=^2pn J r (pn) 2 —pn 



Arm of resisting couple, 



,=1-3* 



(1) 



(2) 



(For f= 15,000 to 16,000, and/ c =600fc> 650, k may be taken at |.) 
Fiber stresses, 



_ M M 

J s Ajd pjbd 2 



2J£_2pf E 
jkbcP' 






(3) 
(4) 



Steel ratio, for balanced reinforcement, 

1 1 




Case 17 When the neutral axis lies in the flange, use the formulas for 
rectangular beams. 

Case II. When the neutral axis lies in the stem, the following formulas 
neglect the compression in the stem: 

Position of neutral axis, 

2ndA+bt 2 



M ~2nA +2bt 
Position of resultant compression, 

Z ~2kd- t 3 



(6) 

(7) 



Arm of resisting couple, 
Fiber stresses, 

/c = 



jd=d—z 

f-JL 

J *~Ajd 

Mid _/ s 



bt(kd-$t)jd n 1-k 



(8) 

(9) 
(10) 



(For approximate results the formulas for rectangular beams may 
be used.) 

The following formulas take into account the compression in the 
stem; they are recommended where the flange is small compared 
with the stem: 

Position of neutral axis, 



+ 



M= l 2 nd A +(b- b')t 2 , /n4+(&-&')*V nA+(b-b')t 
Position of resultant compression, 



V 



Z== t(2kd-t)b+(kd-t) 2 b' 

Arm of resisting couple, 

jd=d— z 

Fiber stresses, 

/s Ajd 
2 Mkd 



/o=i 



[(2kd-t)bt+(kd-t) 2 l/]jd 

3. Beams Reinforced for Compression. 



c+e 




(ii) 

(12) 

(13) 

.(14) 
(15) 



10 

Position of neutral axis, 



(17) 



k=j2n(p+p / ^+n\ P +v / ) 2 -n{ V +p / ) (16) 

Position of resultant compression, 

P+2/n(/:-f) 

Arm of resisting couple, 

jd=d-z (18) 

Fiber stresses, 

63/ 



/c= 



bd 



(19) 



/■— ^L=nf — ( 2 °) 

4. Shear, Bond, and Web Reinforcement. 

In the following formulas S refers only to the bars constituting 
the tension reinforcement at the section in question, and jd is the 
lever arm of the resisting couple at the section. 

For rectangular beams. 



v= Wd 



(22) 



U =jd2 



(23) 



(For approximate results j may be taken as £.) > 

The stresses in web reinforcement may be estimated by the fol- 



lowing formulas: 

Vertical web reinforcement. 



p-S ( 24 ) 

id 



Web reinforcement inclined at 45° (not bent-up bars) 

Vs 

Jd 



P=0.7 F ! (25) 



11 

in which P=stress in single reinforcing member, F=amount of total 
shear assumed as carried by the reinforcement, and s=horizontal 
spacing of the reinforcing members. 

The same formulas apply to beams reinforced for compression as 
regards shear and bond stress for tensile steel. 

For T beams, 

-fS (26) 



V 


(27) 


(For approximate results j may be taken at f .) 




5. Columns. 
Total safe load, 




P=f (A B +nA 3 )=f c A[l+(n-l)p] 
Unit stresses, 

Jc A[l+(n-l)p] 


(28) 

(29) 


f s = nfc 


(30) 



THE FLAT SLAB FLOOR WITHOUT BEAMS. 

1. Symbols for Square Panels. 

Z=distance center to center of columns in feet measured 
along the side of a square panel. 

C= diameter of column capital in feet measured on the 
bottom surface of the slab or dropped panel. 

#=side of square dropped panel in feet. 

B= width of any band of rods in feet. 

Tf=sum of live and dead loads in pounds per square foot. 

J/=bending moment in foot-pounds. 

d= effective depth of slab in inches. 

D= effective depth of dropped panel in inches. 
£=total thickness of s!ab in inches. 

T=total thickness of dropped panel in inches. Other sym- 
bols are those used in the Standard Notation. 

2. Four-Way System With Dropped Panel. 

The fo 1 lowing formulas shall be used in design: 

S=0A2l 

C=0.225Z 

B=0A2l 

d=l'iJ?h. on basis of moment, for w not greater than 440 

pounds and p=0.77 per cent. 

wl 
d= on basis of sheer, for w greater than 440 pounds. 

D=l.bd! 

t=d-\-l.b inches. 
T=D+2 inches. 



12 

Total negative iYat column (in any direction)=0.032i(;Z 3 . 

Positive i/at middle of bands=0.012?/;Z 3 . 

Negative If over middle of side bands= 0.009 wl 3 . 

Note. — The above proportions for S, C, B, and D make it neces- 
sary to solve only two of the other formulas. Assume a total thick- 
ness, t, to determine a tentative value of w. Solve for d and deter- 
mine the correct value of w. D then becomes 1.5<1 Find the posi- 
tive moment at the middle of the bands from the formula positive 
M—0.012wl 3 . From the moment thus found find the amount of 
positive steel required at the middle of each band. Carry this same 
amount of steel over the column in each band, which will take care 
of the total negative moment at the column. Finally, take three- 
fourths of this positive steel and distribute it in the top of the slab 
over the side bands and over the central half of the panel to take 
care of the negative moment at the middle of the side bands. 

3. Two-Way System With Dropped Panel. 

The following formulas shall be used in design: 
S=0Al. 
C=0.225Z. 
B=0AL_ 

d= l±^±on basis of moment, for w not greater than 576 
50 
pounds and p=0.77 per cent. 

wl 
<?= -, 2qa > on basis of shear, for w greater than 576 pounds. 

D=1.2bd, for p=l per cent. 
t=d+l.b inches. 

T=D+2 inches. 
Negative M at column for each band=0.032w>Z 3 . 
Positive i/at middle of side band = 0.01 7 wl 3 . 
Negative i/over middle of side band=0.015wZ 3 . 
Positive M at middle of center band=0.008w;Z 3 . 

4. Details of Construction. 

The above formulas apply to square panels and uniformly dis- 
tributed live loads. For heavy concentrated loads special provision 
will have to be made by the use of beams or girders. 

The diameter of the column capital shall be considered to be meas- 
ured where its vertical thickness is at least 1 1/2 inches, provided 
the slope of the capital below this point nowhere makes an angle 
with the vertical of more than 45 degrees. 

Points of inflection on any line joining two column centers may 
be taken as one-fifth of the clear distance on that line between the 
perimeters of the column capitals and measured from the perime- 
ters. 

If the length of end panels is made equal to 0.85 of the length of 
interior panels, it will not be necessary to compute the moments 
for end panels, and the same distribution of steel may be used in 
both end and interior panels. 



13 

Punching shear at the face of the column shall not exceed 120 
pounds per square inch. 
The total thickness of the slab shall never be less than 6 inches. 

5. Rectangular Panels With Unequal Sides. 

The following applies to both the four-way and the two-way 
systems: 

In determining the thickness of slabs and dropped panels the 
factor I, occurring in the formulas for thickness, shall be the longest 
side distance center to center of columns. 

In determining moments in side bands and center bands the 
factor I, occurring in the formulas for moments, shall be the distance 
center to center of columns parallel to the band in question. 

In determining moments in diagonal bands the factor I, occurring 
in the formulas for moments, shall be the average of the two side 
distances center to center of columns. 

o 



LIBRARY OF CONGRESS 



021 604 934 2 f 



I 




021 604 934 2 



